Cancer drug testing in animals is an extremely poor predictor of the drug's safety and efficacy observed in humans. Hence there is a pressing need for functional testing platforms that better predict traditional and immunotherapy responses in human, live tumor tissue or tissue constructs, and at the same time are compatible with the use of mouse tumor tissue to facilitate building more accurate disease models. Since many cancer drug actions rely on mechanisms that depend on the tumor microenvironment (TME), such platforms should also retain as much of the native TME as possible. Additionally, platforms based on miniaturization technologies are desirable to reduce animal use and sensitivity to human tissue scarcity. Present high-throughput testing platforms that have some of these features, e.g. based on patient-derived tumor organoids, require a growth step that alters the TME. On the other hand, microdissected tumors (μDTs) or "spheroids" that retain an intact TME have shown promising responses to immunomodulators acting on native immune cells. However, difficult tissue handling after microdissection has reduced the throughput of drug testing on μDTs, thereby constraining the inherent advantages of producing numerous TME-preserving units of tissue for drug testing. Here we demonstrate a microfluidic 96-well platform designed for drug treatment of hundreds of similarly-sized, cuboidal μDTs ("cuboids") produced from a single tumor sample. The platform organizes a monodisperse array of four cuboids per well in 384 hydrodynamic traps. The microfluidic device, entirely fabricated in thermoplastics, features 96 microvalves that fluidically isolate each well after the cuboid loading step for straightforward multi-drug testing. Since our platform makes the most of scarce tumor tissue, it can potentially be applied to human biopsies that preserve the human TME while minimizing animal testing.